In　this　paper,　an　optimized　formation　control　based　on　single　critic　reinforcement　learning　is　developed　for　a　class　of　second-order　multi-agent　systems.　Unlike　first-order　systems,　both　position　and　velocity　variables　need　to　be　considered　in　second-order　system　control.　Therefore,　the　control　of　second-order　systems　is　more　challenging.　In　the　control　design,　single　critic　reinforcement　learning　method　combined　with　fuzzy　logic　systems　is　used.　Fuzzy　logic　systems　approximator　is　used　to　compensate　the　nonlinearity　of　the　systems.　Compared　with　the　actor-critic　reinforcement　learning　method,　single　critic　reinforcement　learning　requires　only　one　network　iterative　training　such　that　the　training　errors　are　smaller,　and　the　calculation　time　caused　by　the　iterative　loop　between　actor　and　critic　can　be　reduced.　According　to　the　analysis　of　Lyapunov　stability　theory,　the　proposed　control　design　can　achieve　the　control　objective.　Finally,　the　effectiveness　of　the　proposed　method　is　verified　by　simulation.　©　2021　IEEE.